155 research outputs found
Dynamical properties of the Zhang model of Self-Organized Criticality
Critical exponents of the infinitely slowly driven Zhang model of
self-organized criticality are computed for with particular emphasis
devoted to the various roughening exponents. Besides confirming recent
estimates of some exponents, new quantities are monitored and their critical
exponents computed. Among other results, it is shown that the three dimensional
exponents do not coincide with the Bak, Tang, and Wiesenfeld (abelian) model
and that the dynamical exponent as computed from the correlation length and
from the roughness of the energy profile do not necessarily coincide as it is
usually implicitly assumed. An explanation for this is provided. The
possibility of comparing these results with those obtained from Renormalization
Group arguments is also briefly addressed.Comment: 8 pages, 12 PostScript figures, RevTe
A numerical study of one-patch colloidal particles: from square-well to Janus
We perform numerical simulations of a simple model of one-patch colloidal
particles to investigate: (i) the behavior of the gas-liquid phase diagram on
moving from a spherical attractive potential to a Janus potential and (ii) the
collective structure of a system of Janus particles. We show that, for the case
where one of the two hemispheres is attractive and one is repulsive, the system
organizes into a dispersion of orientational ordered micelles and vesicles and,
at low , the system can be approximated as a fluid of such clusters,
interacting essentially via excluded volume. The stability of this cluster
phase generates a very peculiar shape of the gas and liquid coexisting
densities, with a gas coexistence density which increases on cooling,
approaching the liquid coexistence density at very low .Comment: 9 pages, 10 figures, Phys. Chem. Chem. Phys. in press (2010
Bridging and depletion mechanisms in colloid-colloid effective interactions: A reentrant phase diagram
A general class of nonadditive sticky-hard-sphere binary mixtures, where
small and large spheres represent the solvent and the solute, respectively, is
introduced. The solute-solute and solvent-solvent interactions are of
hard-sphere type, while the solute-solvent interactions are of
sticky-hard-sphere type with tunable degrees of size nonadditivity and
stickiness. Two particular and complementary limits are studied using
analytical and semi-analytical tools. The first case is characterized by zero
nonadditivity, lending itself to a Percus-Yevick approximate solution from
which the impact of stickiness on the spinodal curves and on the effective
solute-solute potential is analyzed. In the opposite nonadditive case, the
solvent-solvent diameter is zero and the model can then be reckoned as an
extension of the well-known Asakura-Oosawa model with additional sticky
solute-solvent interaction. This latter model has the property that its exact
effective one-component problem involves only solute-solute pair potentials for
size ratios such that a solvent particle fits inside the interstitial region of
three touching solutes. In particular, we explicitly identify the three
competing physical mechanisms (depletion, pulling, and bridging) giving rise to
the effective interaction. Some remarks on the phase diagram of these two
complementary models are also addressed through the use of the Noro-Frenkel
criterion and a first-order perturbation analysis. Our findings suggest
reentrance of the fluid-fluid instability as solvent density (in the first
model) or adhesion (in the second model) is varied. Some perspectives in terms
of the interpretation of recent experimental studies of microgels adsorbed onto
large polystyrene particles are discussed.Comment: 16 pages, 11 figures; v2: Fig. 3 replaced by a different one, panels
(c) and (d) of Fig. 9 added, plus other minor change
Collective dynamics in coupled maps on a lattice with quenched disorder
It is investigated how a spatial quenched disorder modifies the dynamics of
coupled map lattices. The disorder is introduced via the presence or absence of
coupling terms among lattice sites. Two nonlinear maps have been considered
embodying two paradigmatic dynamics. The Miller and Huse map can be associated
with an Ising-like dynamics, whereas the logistic coupled maps is a prototype
of a non trivial collective dynamics. Various indicators quantifying the
overall behavior, demonstrates that even a small amount of spatial disorder is
capable to alter the dynamics found for purely ordered cases.Comment: 27 pages, 15 figures, accepted for publication in Phys. Rev.
Structure factors for the simplest solvable model of polydisperse colloidal fluids with surface adhesion
Closed analytical expressions for scattering intensity and other global
structure factors are derived for a new solvable model of polydisperse sticky
hard spheres. The starting point is the exact solution of the ``mean spherical
approximation'' for hard core plus Yukawa potentials, in the limit of infinite
amplitude and vanishing range of the attractive tail, with their product
remaining constant. The choice of factorizable coupling (stickiness) parameters
in the Yukawa term yields a simpler ``dyadic structure'' in the Fourier
transform of the Baxter factor correlation function , with a
remarkable simplification in all structure functions with respect to previous
works. The effect of size and stickiness polydispersity is analyzed and
numerical results are presented for two particular versions of the model: i)
when all polydisperse particles have a single, size-independent, stickiness
parameter, and ii) when the stickiness parameters are proportional to the
diameters. The existence of two different regimes for the average structure
factor, respectively above and below a generalized Boyle temperature which
depends on size polydispersity, is recognized and discussed. Because of its
analycity and simplicity, the model may be useful in the interpretation of
small-angle scattering experimental data for polydisperse colloidal fluids of
neutral particles with surface adhesion.Comment: 32 pages, 7 figures, RevTex style, to appear in J. Chem. Phys. 1
December 200
Stability boundaries, percolation threshold, and two phase coexistence for polydisperse fluids of adhesive colloidal particles
We study the polydisperse Baxter model of sticky hard spheres (SHS) in the
modified Mean Spherical Approximation (mMSA). This closure is known to be the
zero-order approximation (C0) of the Percus-Yevick (PY) closure in a density
expansion. The simplicity of the closure allows a full analytical study of the
model. In particular we study stability boundaries, the percolation threshold,
and the gas-liquid coexistence curves. Various possible sub-cases of the model
are treated in details. Although the detailed behavior depends upon the
particularly chosen case, we find that, in general, polydispersity inhibits
instabilities, increases the extent of the non percolating phase, and
diminishes the size of the gas-liquid coexistence region. We also consider the
first-order improvement of the mMSA (C0) closure (C1) and compare the
percolation and gas-liquid boundaries for the one-component system with recent
Monte Carlo simulations. Our results provide a qualitative understanding of the
effect of polydispersity on SHS models and are expected to shed new light on
the applicability of SHS models for colloidal mixtures.Comment: 37 pages, 7 figures, 1 tabl
Pathologies in the sticky limit of hard-sphere-Yukawa models for colloidal fluids. A possible correction
A known `sticky-hard-sphere' model, defined starting from a
hard-sphere-Yukawa potential and taking the limit of infinite amplitude and
vanishing range with their product remaining constant, is shown to be
ill-defined. This is because its Hamiltonian (which we call SHS2) leads to an
{\it exact}second virial coefficient which {\it diverges}, unlike that of
Baxter's original model (SHS1). This deficiency has never been observed so far,
since the linearization implicit in the `mean spherical approximation' (MSA),
within which the model is analytically solvable, partly {\it masks} such a
pathology. To overcome this drawback and retain some useful features of SHS2,
we propose both a new model (SHS3) and a new closure (`modified MSA'), whose
combination yields an analytic solution formally identical with the SHS2-MSA
one. This mapping allows to recover many results derived from SHS2, after a
re-interpretation within a correct framework. Possible developments are finally
indicated.Comment: 21 pages, 1 figure, accepted in Molecular Physics (2003
Flory theory for Polymers
We review various simple analytical theories for homopolymers within a
unified framework. The common guideline of our approach is the Flory theory,
and its various avatars, with the attempt of being reasonably self-contained.
We expect this review to be useful as an introduction to the topic at the
graduate students level.Comment: Topical review appeared J. Phys.: Condens. Matter, 46 pages, 8
Figures. Sec. VIF added. Typos fixed. Few references adde
Fluid-Fluid and Fluid-Solid transitions in the Kern-Frenkel model from Barker-Henderson thermodynamic perturbation theory
We study the Kern-Frenkel model for patchy colloids using Barker-Henderson
second-order thermodynamic perturbation theory. The model describes a fluid
where hard sphere particles are decorated with one patch, so that they interact
via a square-well (SW) potential if they are sufficiently close one another,
and if patches on each particle are properly aligned. Both the gas-liquid and
fluid-solid phase coexistences are computed and contrasted against
corresponding Monte-Carlo simulations results. We find that the perturbation
theory describes rather accurately numerical simulations all the way from a
fully covered square-well potential down to the Janus limit (half coverage). In
the region where numerical data are not available (from Janus to hard-spheres),
the method provides estimates of the location of the critical lines that could
serve as a guideline for further efficient numerical work at these low
coverages. A comparison with other techniques, such as integral equation
theory, highlights the important aspect of this methodology in the present
context.Comment: Accepted for publication in The Journal of Chemical Physics (2012
Penetrable-Square-Well fluids: Analytical study and Monte Carlo simulations
We study structural and thermophysical properties of a one-dimensional
classical fluid made of penetrable spheres interacting via an attractive
square-well potential. Penetrability of the spheres is enforced by reducing
from infinite to finite the repulsive energy barrier in the pair potentials As
a consequence, an exact analytical solution is lacking even in one dimension.
Building upon previous exact analytical work in the low-density limit [Santos
\textit{et al.}, Phys. Rev. E \text{77}, 051206 (2008)], we propose an
approximate theory valid at any density and in the low-penetrable regime. By
comparison with specialized Monte Carlo simulations and integral equation
theories, we assess the regime of validity of the theory. We investigate the
degree of inconsistency among the various routes to thermodynamics and explore
the possibility of a fluid-fluid transition. Finally we locate the dependence
of the Fisher-Widom line on the degree of penetrability. Our results constitute
the first systematic study of penetrable spheres with attractions as a
prototype model for soft systems.Comment: 26 pages and 9 figure
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